Subgroups — C₄₃×#7616 #24927633

Order 11008.

634 conjugacy classes of subgroups.

The subgroup lattice has 434 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×#121×C₄₃	C₂	1	1	yes	maximal, characteristic
2	C₄₃×#1797	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄₃×#1728	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄₃×#1271	C₂	1	2	yes	maximal, complemented
5	C₄₃×#1270	C₂	1	2	yes	maximal, complemented
6	C₂²×M₁₆×C₄₃	—	2	1	no	—
7	C₂×#121×C₄₃	C₄	1	1	yes	characteristic
8	C₂×C₄×D₄×C₄₃	—	2	1	no	—
9	C₂×C₄×D₄×C₄₃	C₄	1	1	yes	characteristic
10	C₂²×C₄²×C₄₃	C₂²	1	1	yes	characteristic
11	C₂×C₄⋊C₈×C₄₃	—	2	1	no	—
12	C₂×C₂²⋊C₈×C₄₃	—	2	1	no	—
13	C₄₃×#390	C₂²	1	1	yes	characteristic
14	C₄₃×#389	C₂²	1	1	yes	characteristic
15	C₄₃×#388	—	2	1	no	—
16	C₄₃×#386	—	2	1	no	—
17	C₄₃×#380	C₄	1	1	yes	characteristic
18	C₄×C₄⋊C₄×C₄₃	C₄	1	1	yes	characteristic
19	C₄×C₂²⋊C₄×C₄₃	—	2	1	no	—
20	C₄₃×#336	—	2	1	no	—
21	C₄₃×#336	C₂²	1	2	yes	—
22	C₄₃×#336	C₂²	1	2	yes	—
23	C₂²×D₄×C₄₃	—	2	1	no	—
24	C₂²×D₄×C₄₃	C₂×C₄	1	1	yes	characteristic
25	C₂³×C₄×C₄₃	—	2	1	no	—
26	C₂³×C₄×C₄₃	C₂×C₄	1	1	yes	characteristic
27	C₂³×C₄×C₄₃	D₄	1	1	yes	characteristic
28	C₂³×C₄×C₄₃	D₄	1	1	yes	characteristic
29	C₂×M₁₆×C₄₃	—	2	4	no	—
30	C₂×M₁₆×C₄₃	—	4	2	no	—
31	C₂×M₁₆×C₄₃	—	4	2	no	—
32	C₂²×C₈×C₄₃	—	2	2	no	—
33	C₂²×C₈×C₄₃	—	2	2	no	—
34	#121×C₄₃	—	2	2	no	—
35	#121×C₄₃	—	2	2	no	—
36	C₄×D₄×C₄₃	—	4	2	no	—
37	C₄×D₄×C₄₃	—	4	2	no	—
38	C₄×D₄×C₄₃	—	4	2	no	—
39	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
40	C₂×C₄⋊C₄×C₄₃	C₂×C₄	1	1	yes	characteristic
41	C₂×C₄⋊C₄×C₄₃	C₂×C₄	1	1	yes	characteristic
42	C₂×C₄⋊C₄×C₄₃	C₂×C₄	1	1	yes	characteristic
43	C₂×C₂²⋊C₄×C₄₃	—	2	1	no	—
44	C₂×C₂²⋊C₄×C₄₃	—	2	1	no	—
45	C₂×C₂²⋊C₄×C₄₃	—	2	1	no	—
46	C₂×C₂²⋊C₄×C₄₃	—	2	1	no	—
47	C₂×C₂²⋊C₄×C₄₃	—	2	1	no	—
48	C₂×C₄²×C₄₃	—	2	1	no	—
49	C₂×C₄²×C₄₃	—	4	2	no	—
50	C₂×C₄²×C₄₃	C₂×C₄	1	1	yes	characteristic
51	C₂×C₄²×C₄₃	D₄	1	1	yes	characteristic
52	C₂×C₄²×C₄₃	D₄	1	1	yes	characteristic
53	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
54	C₄⋊C₈×C₄₃	—	4	2	no	—
55	C₂²⋊C₈×C₄₃	—	4	2	no	—
56	#95×C₄₃	—	2	1	no	—
57	#95×C₄₃	—	2	1	no	—
58	#95×C₄₃	—	2	1	no	—
59	C₂⁴×C₄₃	—	2	1	no	—
60	C₂⁴×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
61	C₂×D₄×C₄₃	—	2	4	no	—
62	C₂×D₄×C₄₃	—	2	1	no	—
63	C₂×D₄×C₄₃	—	4	2	no	—
64	C₂×D₄×C₄₃	—	4	2	no	—
65	C₂×D₄×C₄₃	—	4	1	no	—
66	C₂×D₄×C₄₃	—	4	1	no	—
67	C₂×D₄×C₄₃	M₁₆	1	2	yes	complemented
68	C₂²×C₄×C₄₃	—	2	2	no	—
69	C₂²×C₄×C₄₃	—	2	2	no	—
70	C₂²×C₄×C₄₃	—	2	1	no	—
71	C₂²×C₄×C₄₃	—	2	1	no	—
72	C₂²×C₄×C₄₃	—	2	1	no	—
73	C₂²×C₄×C₄₃	—	2	1	no	—
74	C₂²×C₄×C₄₃	—	2	1	no	—
75	C₂²×C₄×C₄₃	—	2	1	no	—
76	C₂²×C₄×C₄₃	—	2	1	no	—
77	C₂²×C₄×C₄₃	—	4	1	no	—
78	C₂²×C₄×C₄₃	—	4	1	no	—
79	C₂²×C₄×C₄₃	—	4	1	no	—
80	C₂²×C₄×C₄₃	—	4	1	no	—
81	C₂²×C₄×C₄₃	—	4	2	no	—
82	C₂²×C₄×C₄₃	—	4	2	no	—
83	C₂²×C₄×C₄₃	—	4	2	no	—
84	C₂²×C₄×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
85	C₂²×C₄×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
86	C₂²×C₄×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
87	C₂²×C₄×C₄₃	D₈	1	2	yes	—
88	C₂²×C₄×C₄₃	SD₁₆	1	2	yes	—
89	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
90	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
91	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
92	M₁₆×C₄₃	—	4	8	no	—
93	C₂×C₈×C₄₃	—	2	4	no	—
94	C₂×C₈×C₄₃	—	4	2	no	—
95	C₂×C₈×C₄₃	—	4	2	no	—
96	C₂×C₈×C₄₃	—	4	2	no	—
97	C₂×C₈×C₄₃	—	4	2	no	—
98	C₂×C₈×C₄₃	—	4	2	no	—
99	C₄⋊C₄×C₄₃	—	2	1	no	—
100	C₄⋊C₄×C₄₃	—	4	1	no	—
101	C₄⋊C₄×C₄₃	—	4	1	no	—
102	C₄⋊C₄×C₄₃	—	4	1	no	—
103	C₄⋊C₄×C₄₃	—	4	1	no	—
104	C₄⋊C₄×C₄₃	M₁₆	1	2	yes	complemented
105	C₂²⋊C₄×C₄₃	—	2	4	no	—
106	C₂²⋊C₄×C₄₃	—	4	2	no	—
107	C₂²⋊C₄×C₄₃	—	4	1	no	—
108	C₂²⋊C₄×C₄₃	—	4	1	no	—
109	C₂²⋊C₄×C₄₃	—	4	1	no	—
110	C₂²⋊C₄×C₄₃	—	4	1	no	—
111	C₂²⋊C₄×C₄₃	—	4	2	no	—
112	C₄²×C₄₃	—	2	2	no	—
113	C₄²×C₄₃	—	2	2	no	—
114	C₄²×C₄₃	—	4	1	no	—
115	C₄²×C₄₃	—	4	1	no	—
116	C₄²×C₄₃	—	4	2	no	—
117	C₂³×C₄₃	—	2	1	no	—
118	C₂³×C₄₃	—	2	1	no	—
119	C₂³×C₄₃	—	2	1	no	—
120	C₂³×C₄₃	—	2	1	no	—
121	C₂³×C₄₃	—	2	1	no	—
122	C₂³×C₄₃	—	2	1	no	—
123	C₂³×C₄₃	—	2	2	no	—
124	C₂³×C₄₃	—	4	1	no	—
125	C₂³×C₄₃	—	4	1	no	—
126	C₂³×C₄₃	—	4	1	no	—
127	C₂³×C₄₃	—	4	1	no	—
128	C₂³×C₄₃	—	4	1	no	—
129	C₂³×C₄₃	—	4	1	no	—
130	C₂³×C₄₃	#102	1	2	yes	—
131	C₂³×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
132	D₄×C₄₃	—	4	2	no	—
133	D₄×C₄₃	—	4	2	no	—
134	D₄×C₄₃	—	4	8	no	—
135	C₂×C₄×C₄₃	—	2	1	no	—
136	C₂×C₄×C₄₃	—	2	1	no	—
137	C₂×C₄×C₄₃	—	2	1	no	—
138	C₂×C₄×C₄₃	—	2	1	no	—
139	C₂×C₄×C₄₃	—	2	1	no	—
140	C₂×C₄×C₄₃	—	2	1	no	—
141	C₂×C₄×C₄₃	—	2	4	no	—
142	C₂×C₄×C₄₃	—	2	4	no	—
143	C₂×C₄×C₄₃	—	2	1	no	—
144	C₂×C₄×C₄₃	—	2	2	no	—
145	C₂×C₄×C₄₃	—	2	1	no	—
146	C₂×C₄×C₄₃	—	2	1	no	—
147	C₂×C₄×C₄₃	—	2	1	no	—
148	C₂×C₄×C₄₃	—	2	1	no	—
149	C₂×C₄×C₄₃	—	2	1	no	—
150	C₂×C₄×C₄₃	—	4	2	no	—
151	C₂×C₄×C₄₃	—	4	2	no	—
152	C₂×C₄×C₄₃	—	4	2	no	—
153	C₂×C₄×C₄₃	—	4	2	no	—
154	C₂×C₄×C₄₃	—	4	1	no	—
155	C₂×C₄×C₄₃	—	4	1	no	—
156	C₂×C₄×C₄₃	—	4	1	no	—
157	C₂×C₄×C₄₃	—	4	1	no	—
158	C₂×C₄×C₄₃	—	4	1	no	—
159	C₂×C₄×C₄₃	—	4	1	no	—
160	C₂×C₄×C₄₃	—	4	1	no	—
161	C₂×C₄×C₄₃	—	4	1	no	—
162	C₂×C₄×C₄₃	—	8	4	no	—
163	C₂×C₄×C₄₃	#99	1	2	yes	—
164	C₂×C₄×C₄₃	#102	1	2	yes	—
165	C₂×C₄×C₄₃	#104	1	2	yes	—
166	C₂×C₄×C₄₃	C₂×M₁₆	1	1	yes	characteristic
167	C₂×C₄×C₄₃	C₂×M₁₆	1	1	yes	characteristic
168	C₂×C₄×C₄₃	C₂×D₈	1	1	yes	characteristic
169	C₂×C₄×C₄₃	C₂×SD₁₆	1	1	yes	characteristic
170	C₂×C₄×C₄₃	AGL(1,ℤ/8)	1	1	yes	characteristic
171	C₂×C₄×C₄₃	#137	1	1	yes	characteristic
172	C₈×C₄₃	—	4	4	no	—
173	C₈×C₄₃	—	8	2	no	—
174	#7616	C₄₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
175	C₂²×C₄₃	—	2	2	no	—
176	C₂²×C₄₃	—	2	2	no	—
177	C₂²×C₄₃	—	2	2	no	—
178	C₂²×C₄₃	—	4	1	no	—
179	C₂²×C₄₃	—	4	1	no	—
180	C₂²×C₄₃	—	4	1	no	—
181	C₂²×C₄₃	—	4	1	no	—
182	C₂²×C₄₃	—	4	2	no	—
183	C₂²×C₄₃	—	4	2	no	—
184	C₂²×C₄₃	—	4	2	no	—
185	C₂²×C₄₃	—	8	1	no	—
186	C₂²×C₄₃	—	8	1	no	—
187	C₂²×C₄₃	—	8	1	no	—
188	C₂²×C₄₃	—	8	1	no	—
189	C₂²×C₄₃	#407	1	1	yes	characteristic
190	C₂²×C₄₃	C₂×#99	1	1	yes	characteristic
191	C₂²×C₄₃	#413	1	1	yes	characteristic
192	C₂²×C₄₃	C₂×#102	1	1	yes	characteristic
193	C₂²×C₄₃	#417	1	1	yes	characteristic
194	C₂²×C₄₃	C₂×#104	1	1	yes	characteristic
195	C₂²×C₄₃	#421	1	1	yes	characteristic
196	C₄×C₄₃	—	2	1	no	—
197	C₄×C₄₃	—	2	1	no	—
198	C₄×C₄₃	—	2	1	no	—
199	C₄×C₄₃	—	2	1	no	—
200	C₄×C₄₃	—	2	1	no	—
201	C₄×C₄₃	—	2	1	no	—
202	C₄×C₄₃	—	4	1	no	—
203	C₄×C₄₃	—	4	2	no	—
204	C₄×C₄₃	—	4	1	no	—
205	C₄×C₄₃	—	8	1	no	—
206	C₄×C₄₃	—	8	1	no	—
207	C₄×C₄₃	#327	1	4	yes	—
208	C₄×#121	C₂×C₄₃	1	1	yes	characteristic
209	#1797	C₂×C₄₃	1	1	yes	characteristic, complemented
210	#1728	C₂×C₄₃	1	1	yes	characteristic, complemented
211	#1271	C₂×C₄₃	1	2	yes	complemented
212	#1270	C₂×C₄₃	1	2	yes	complemented
213	C₂×C₄₃	—	4	2	no	—
214	C₂×C₄₃	—	8	2	no	—
215	C₂×C₄₃	#1465	1	1	yes	characteristic
216	C₂×C₄₃	#1486	1	1	yes	characteristic
217	C₂×C₄₃	#1489	1	1	yes	characteristic
218	C₂×C₄₃	C₂×#327	1	1	yes	characteristic
219	C₂×C₄₃	#1513	1	1	yes	characteristic
220	C₂×C₄₃	#1529	1	1	yes	characteristic
221	C₂×C₄₃	#1547	1	1	yes	characteristic
222	C₂²×M₁₆	—	2	1	no	—
223	C₂×#121	C₄×C₄₃	1	1	yes	characteristic
224	C₂×C₄×D₄	—	2	1	no	—
225	C₂×C₄×D₄	C₄×C₄₃	1	1	yes	characteristic
226	C₂²×C₄²	C₂²×C₄₃	1	1	yes	characteristic
227	C₂×C₄⋊C₈	—	2	1	no	—
228	C₂×C₂²⋊C₈	—	2	1	no	—
229	#390	C₂²×C₄₃	1	1	yes	characteristic
230	#389	C₂²×C₄₃	1	1	yes	characteristic
231	#388	—	2	1	no	—
232	#386	—	2	1	no	—
233	#380	C₄×C₄₃	1	1	yes	characteristic
234	C₄×C₄⋊C₄	C₄×C₄₃	1	1	yes	characteristic
235	C₄×C₂²⋊C₄	—	2	1	no	—
236	#336	—	2	1	no	—
237	#336	C₂²×C₄₃	1	2	yes	—
238	#336	C₂²×C₄₃	1	2	yes	—
239	C₄₃	#7616	1	1	yes	characteristic, direct product factor, Sylow
240	C₂²×D₄	—	2	1	no	—
241	C₂²×D₄	C₂×C₄×C₄₃	1	1	yes	characteristic
242	C₂³×C₄	—	2	1	no	—
243	C₂³×C₄	C₂×C₄×C₄₃	1	1	yes	characteristic
244	C₂³×C₄	D₄×C₄₃	1	1	yes	characteristic
245	C₂³×C₄	D₄×C₄₃	1	1	yes	characteristic
246	C₂×M₁₆	—	2	4	no	—
247	C₂×M₁₆	—	4	2	no	—
248	C₂×M₁₆	—	4	2	no	—
249	C₂²×C₈	—	2	2	no	—
250	C₂²×C₈	—	2	2	no	—
251	#121	—	2	2	no	—
252	#121	—	2	2	no	—
253	C₄×D₄	—	4	2	no	—
254	C₄×D₄	—	4	2	no	—
255	C₄×D₄	—	4	2	no	—
256	C₂×C₄⋊C₄	—	2	1	no	—
257	C₂×C₄⋊C₄	C₂×C₄×C₄₃	1	1	yes	characteristic
258	C₂×C₄⋊C₄	C₂×C₄×C₄₃	1	1	yes	characteristic
259	C₂×C₄⋊C₄	C₂×C₄×C₄₃	1	1	yes	characteristic
260	C₂×C₂²⋊C₄	—	2	1	no	—
261	C₂×C₂²⋊C₄	—	2	1	no	—
262	C₂×C₂²⋊C₄	—	2	1	no	—
263	C₂×C₂²⋊C₄	—	2	1	no	—
264	C₂×C₂²⋊C₄	—	2	1	no	—
265	C₂×C₄²	—	2	1	no	—
266	C₂×C₄²	—	4	2	no	—
267	C₂×C₄²	C₂×C₄×C₄₃	1	1	yes	characteristic
268	C₂×C₄²	D₄×C₄₃	1	1	yes	characteristic
269	C₂×C₄²	D₄×C₄₃	1	1	yes	characteristic
270	C₂×C₄²	C₂³×C₄₃	1	1	yes	characteristic
271	C₄⋊C₈	—	4	2	no	—
272	C₂²⋊C₈	—	4	2	no	—
273	#95	—	2	1	no	—
274	#95	—	2	1	no	—
275	#95	—	2	1	no	—
276	C₂⁴	—	2	1	no	—
277	C₂⁴	C₂²⋊C₄×C₄₃	1	1	yes	characteristic
278	C₂×D₄	—	2	4	no	—
279	C₂×D₄	—	2	1	no	—
280	C₂×D₄	—	4	1	no	—
281	C₂×D₄	—	4	1	no	—
282	C₂×D₄	—	4	2	no	—
283	C₂×D₄	—	4	2	no	—
284	C₂×D₄	M₁₆×C₄₃	1	2	yes	complemented
285	C₂²×C₄	—	2	2	no	—
286	C₂²×C₄	—	2	2	no	—
287	C₂²×C₄	—	2	1	no	—
288	C₂²×C₄	—	2	1	no	—
289	C₂²×C₄	—	2	1	no	—
290	C₂²×C₄	—	2	1	no	—
291	C₂²×C₄	—	2	1	no	—
292	C₂²×C₄	—	2	1	no	—
293	C₂²×C₄	—	2	1	no	—
294	C₂²×C₄	—	4	1	no	—
295	C₂²×C₄	—	4	1	no	—
296	C₂²×C₄	—	4	1	no	—
297	C₂²×C₄	—	4	1	no	—
298	C₂²×C₄	—	4	2	no	—
299	C₂²×C₄	—	4	2	no	—
300	C₂²×C₄	—	4	2	no	—
301	C₂²×C₄	C₂²⋊C₄×C₄₃	1	1	yes	characteristic
302	C₂²×C₄	C₂²⋊C₄×C₄₃	1	1	yes	characteristic
303	C₂²×C₄	C₂²⋊C₄×C₄₃	1	1	yes	characteristic
304	C₂²×C₄	D₈×C₄₃	1	2	yes	—
305	C₂²×C₄	SD₁₆×C₄₃	1	2	yes	—
306	C₂²×C₄	C₂²×C₄×C₄₃	1	1	yes	characteristic
307	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
308	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
309	M₁₆	—	4	8	no	—
310	C₂×C₈	—	2	4	no	—
311	C₂×C₈	—	4	2	no	—
312	C₂×C₈	—	4	2	no	—
313	C₂×C₈	—	4	2	no	—
314	C₂×C₈	—	4	2	no	—
315	C₂×C₈	—	4	2	no	—
316	C₄⋊C₄	—	2	1	no	—
317	C₄⋊C₄	—	4	1	no	—
318	C₄⋊C₄	—	4	1	no	—
319	C₄⋊C₄	—	4	1	no	—
320	C₄⋊C₄	—	4	1	no	—
321	C₄⋊C₄	M₁₆×C₄₃	1	2	yes	complemented
322	C₂²⋊C₄	—	2	4	no	—
323	C₂²⋊C₄	—	4	2	no	—
324	C₂²⋊C₄	—	4	2	no	—
325	C₂²⋊C₄	—	4	1	no	—
326	C₂²⋊C₄	—	4	1	no	—
327	C₂²⋊C₄	—	4	1	no	—
328	C₂²⋊C₄	—	4	1	no	—
329	C₄²	—	2	2	no	—
330	C₄²	—	2	2	no	—
331	C₄²	—	4	1	no	—
332	C₄²	—	4	1	no	—
333	C₄²	—	4	2	no	—
334	C₂³	—	2	1	no	—
335	C₂³	—	2	1	no	—
336	C₂³	—	2	1	no	—
337	C₂³	—	2	1	no	—
338	C₂³	—	2	1	no	—
339	C₂³	—	2	1	no	—
340	C₂³	—	2	2	no	—
341	C₂³	—	4	1	no	—
342	C₂³	—	4	1	no	—
343	C₂³	—	4	1	no	—
344	C₂³	—	4	1	no	—
345	C₂³	—	4	1	no	—
346	C₂³	—	4	1	no	—
347	C₂³	#102×C₄₃	1	2	yes	—
348	C₂³	C₂×C₂²⋊C₄×C₄₃	1	1	yes	characteristic
349	D₄	—	4	2	no	—
350	D₄	—	4	2	no	—
351	D₄	—	4	8	no	—
352	C₂×C₄	—	2	1	no	—
353	C₂×C₄	—	2	1	no	—
354	C₂×C₄	—	2	1	no	—
355	C₂×C₄	—	2	1	no	—
356	C₂×C₄	—	2	1	no	—
357	C₂×C₄	—	2	1	no	—
358	C₂×C₄	—	2	4	no	—
359	C₂×C₄	—	2	4	no	—
360	C₂×C₄	—	2	1	no	—
361	C₂×C₄	—	2	2	no	—
362	C₂×C₄	—	2	1	no	—
363	C₂×C₄	—	2	1	no	—
364	C₂×C₄	—	2	1	no	—
365	C₂×C₄	—	2	1	no	—
366	C₂×C₄	—	2	1	no	—
367	C₂×C₄	—	4	2	no	—
368	C₂×C₄	—	4	2	no	—
369	C₂×C₄	—	4	2	no	—
370	C₂×C₄	—	4	2	no	—
371	C₂×C₄	—	4	1	no	—
372	C₂×C₄	—	4	1	no	—
373	C₂×C₄	—	4	1	no	—
374	C₂×C₄	—	4	1	no	—
375	C₂×C₄	—	4	1	no	—
376	C₂×C₄	—	4	1	no	—
377	C₂×C₄	—	4	1	no	—
378	C₂×C₄	—	4	1	no	—
379	C₂×C₄	—	8	4	no	—
380	C₂×C₄	#99×C₄₃	1	2	yes	—
381	C₂×C₄	#102×C₄₃	1	2	yes	—
382	C₂×C₄	#104×C₄₃	1	2	yes	—
383	C₂×C₄	C₂×M₁₆×C₄₃	1	1	yes	characteristic
384	C₂×C₄	C₂×M₁₆×C₄₃	1	1	yes	characteristic
385	C₂×C₄	C₂×D₈×C₄₃	1	1	yes	characteristic
386	C₂×C₄	C₂×SD₁₆×C₄₃	1	1	yes	characteristic
387	C₂×C₄	AGL(1,ℤ/8)×C₄₃	1	1	yes	characteristic
388	C₂×C₄	#137×C₄₃	1	1	yes	characteristic
389	C₈	—	4	4	no	—
390	C₈	—	8	2	no	—
391	C₂²	—	2	2	no	—
392	C₂²	—	2	2	no	—
393	C₂²	—	2	2	no	—
394	C₂²	—	4	1	no	—
395	C₂²	—	4	1	no	—
396	C₂²	—	4	1	no	—
397	C₂²	—	4	1	no	—
398	C₂²	—	4	2	no	—
399	C₂²	—	4	2	no	—
400	C₂²	—	4	2	no	—
401	C₂²	—	8	1	no	—
402	C₂²	—	8	1	no	—
403	C₂²	—	8	1	no	—
404	C₂²	—	8	1	no	—
405	C₂²	C₄₃×#407	1	1	yes	characteristic
406	C₂²	C₂×#99×C₄₃	1	1	yes	characteristic
407	C₂²	C₄₃×#413	1	1	yes	characteristic
408	C₂²	C₂×#102×C₄₃	1	1	yes	characteristic
409	C₂²	C₄₃×#417	1	1	yes	characteristic
410	C₂²	C₂×#104×C₄₃	1	1	yes	characteristic
411	C₂²	C₄₃×#421	1	1	yes	characteristic
412	C₄	—	2	1	no	—
413	C₄	—	2	1	no	—
414	C₄	—	2	1	no	—
415	C₄	—	2	1	no	—
416	C₄	—	2	1	no	—
417	C₄	—	2	1	no	—
418	C₄	—	4	1	no	—
419	C₄	—	4	2	no	—
420	C₄	—	4	1	no	—
421	C₄	—	8	1	no	—
422	C₄	—	8	1	no	—
423	C₄	C₄₃×#327	1	4	yes	—
424	C₂	—	4	2	no	—
425	C₂	—	8	2	no	—
426	C₂	C₄₃×#1465	1	1	yes	characteristic
427	C₂	C₄₃×#1486	1	1	yes	characteristic
428	C₂	C₄₃×#1489	1	1	yes	characteristic
429	C₂	C₂×C₄₃×#327	1	1	yes	characteristic
430	C₂	C₄₃×#1513	1	1	yes	characteristic
431	C₂	C₄₃×#1529	1	1	yes	characteristic
432	C₂	C₄₃×#1547	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₄₃	C₂×C₂²⋊C₄
commutator	C₂²×C₄	C₂²×C₄×C₄₃
Frattini, cosocle	C₂×C₄²	C₂³×C₄₃
prime radical	C₂×#121×C₄₃	C₄
LCS	G ▷ C₂²×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₄₃ ◁ C₂²×C₄²×C₄₃ ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
2. C₄₃×#1797	C₂	semidirect
3. C₄₃×#1728	C₂	semidirect
4. C₄₃×#1271	C₂	semidirect
5. C₄₃×#1270	C₂	semidirect
67. C₂×D₄×C₄₃	M₁₆	semidirect
104. C₄⋊C₄×C₄₃	M₁₆	semidirect
174. #7616	C₄₃	direct (N × H)
209. #1797	C₂×C₄₃	semidirect
210. #1728	C₂×C₄₃	semidirect
211. #1271	C₂×C₄₃	semidirect
212. #1270	C₂×C₄₃	semidirect
239. C₄₃	#7616	direct (N × H)
284. C₂×D₄	M₁₆×C₄₃	semidirect
321. C₄⋊C₄	M₁₆×C₄₃	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₄×#121×C₄₃	2
C₄₃×#1797	2
C₄₃×#1728	2
C₄₃×#1271	2
C₄₃×#1270	2
#7616	43

Subgroups — C43×#7616 #24927633

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₃×#7616 #24927633